I cannot get the key off of Neloth at Tel Mithryn that would allow me to get the black book from his locked room. I think my game has a glitch. I am playing on PS3.
The door will only unlock if you complete the quest "Reluctant Steward".
Here is a reference page for the book in question: http://elderscrolls.wikia.com/wiki/Black_Book:_The_Hidden_Twilight_(Book)